Abstract

A simple technique is introduced for measuring the refractive index of plane-parallel samples having thickness of the order of a millimeter. The refractive index values are reported for six bulk semiconductors, each index measured at two infrared wavelengths using this method. The values are found to be within a few percent of those in literature for four semiconductors. The other two semiconductors were newly grown ternary alloys (CdMgTe and CdMnTe), for which the refractive index values have not been reported previously at the wavelengths studied here.

© 2014 Optical Society of America

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  1. D. T. F. Marple, “Refractive index of ZnSe, ZnTe, and CdTe,” J. Appl. Phys. 35, 539–542 (1964).
    [CrossRef]
  2. D. E. Zelmon, E. A. Hanning, and P. G. Schunemann, “Refractive-index measurements and Sellmeier coefficients for zinc germanium phosphide from 2 to 9  μm with implications for phase matching in optical frequency-conversion devices,” J. Opt. Soc. Am. B 18, 1307–1310 (2001).
    [CrossRef]
  3. J. C. Bhattacharya, “Refractive index measurement,” Opt. Laser Technol. 19, 29–32 (1987).
    [CrossRef]
  4. G. D. Gillen and S. Guha, “Use of Michelson and Fabry–Perot interferometry for independent determination of the refractive index and physical thickness of wafers,” Appl. Opt. 44, 344–347 (2005).
    [CrossRef]
  5. G. D. Gillen, C. DiRocco, P. Powers, and S. Guha, “Temperature-dependent refractive index measurements of wafer-shaped InAs and InSb,” Appl. Opt. 47, 164–168 (2008).
    [CrossRef]
  6. H. J. Choi, H. H. Lim, H. S. Moon, T. B. Eom, J. J. Ju, and M. Cha, “Measurement of refractive index and thickness of transparent plate by dual-wavelength interference,” Opt. Express 18, 9429–9434 (2010).
    [CrossRef]
  7. H. Kogelnik and T. Li, “Beams, Modes and Resonators,” in Handbook of Lasers with Selected Data on Optical Technology, R. Pressley, ed. (CRC Press, 1971), pp. 421–441.
  8. F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1957).
  9. S. Guha, “Validity of the paraxial approximation in the focal region of a small-f-number lens,” Opt. Lett. 26, 1598–1600 (2001).
    [CrossRef]
  10. Zemax, LLC, www.zemax.com .
  11. T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94, 6447–6455 (2003).
    [CrossRef]
  12. H. W. Icenogle, B. C. Platt, and W. L. Wolfe, “Refractive indexes and temperature coefficients of germanium and silicon,” Appl. Opt. 15, 2348–2351 (1976).
    [CrossRef]
  13. P. Hlidek, J. Bok, J. Franc, and R. Grill, “Refractive index of CdTe: spectral and temperature dependence,” J. Appl. Phys. 90, 1672–1674 (2001).
    [CrossRef]
  14. S. Adachi, “Optical dispersion relations for GaP, GaAs, GaSb, InP, InAs, InSb, AlxGa1−xAs, and In1−xGaxAsyP1−y,” J. Appl. Phys. 66, 6030–6040 (1989).
    [CrossRef]
  15. From Eq. (1), the refractive index is given by n=(1−Δz/d)−1. With the reasonable assumption that the thickness measurement errors are normally distributed and uncorrelated with Δz, the relative uncertainty δn/n in the refractive index is δnn=n−1(∂n∂dδd)2+(∂n∂ΔzδΔz)2=nd(Δzdδd)2+(δΔz)2.The uncertainty δΔz in the focal shift is given by δΔz=δzsample2+δznosample2≈δz2,where we have explicitly assumed that the focal position measurement error δz is unchanged by the presence of the sample.
  16. A. Hossain, V. Yakimovich, A. E. Bolotnikov, K. Bolton, G. S. Camarda, Y. Cui, J. Franc, R. Gul, K.-H. Kim, H. Pittman, G. Yang, R. Herpst, and R. B. James, “Development of cadmium magnesium telluride (Cd1−xMgxTe) for room temperature X- and gamma-ray detectors,” J. Cryst. Growth 379, 34–40 (2013).
    [CrossRef]
  17. A. Mycielski, A. Burger, M. Sowinska, M. Groza, A. Szadkowski, P. Wojnar, B. Witkowska, W. Kaliszek, and P. Siffert, “Crystal growth and characterization of Cd0.8Mn0.2Te using vertical Bridgman method,” Phys. Status Solidi C 5, 1578–1585 (2005).
  18. L. Kowalczyk, “Second harmonic generation in Cd1−xMnxTe,” J. Cryst. Growth 72, 389–392 (1985).
  19. M. Luttmann, F. Bertin, and A. Chabli, “Optical properties of CdMgTe epitaxial layers: a variable-angle spectroscopic ellipsometry study,” J. Appl. Phys. 78, 3387–3391 (1995).
    [CrossRef]
  20. D. W. Schubert, M. M. Kraus, R. Kenklies, C. R. Becker, and R. N. Bicknell-Tassius, “Composition and wavelength dependence of the refractive index in Cd1−xMnxTe epitaxial layers,” Appl. Phys. Lett. 60, 2192–2194 (1992).
    [CrossRef]
  21. X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).

2013 (1)

A. Hossain, V. Yakimovich, A. E. Bolotnikov, K. Bolton, G. S. Camarda, Y. Cui, J. Franc, R. Gul, K.-H. Kim, H. Pittman, G. Yang, R. Herpst, and R. B. James, “Development of cadmium magnesium telluride (Cd1−xMgxTe) for room temperature X- and gamma-ray detectors,” J. Cryst. Growth 379, 34–40 (2013).
[CrossRef]

2010 (1)

2008 (1)

2005 (2)

G. D. Gillen and S. Guha, “Use of Michelson and Fabry–Perot interferometry for independent determination of the refractive index and physical thickness of wafers,” Appl. Opt. 44, 344–347 (2005).
[CrossRef]

A. Mycielski, A. Burger, M. Sowinska, M. Groza, A. Szadkowski, P. Wojnar, B. Witkowska, W. Kaliszek, and P. Siffert, “Crystal growth and characterization of Cd0.8Mn0.2Te using vertical Bridgman method,” Phys. Status Solidi C 5, 1578–1585 (2005).

2004 (1)

X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).

2003 (1)

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94, 6447–6455 (2003).
[CrossRef]

2001 (3)

1995 (1)

M. Luttmann, F. Bertin, and A. Chabli, “Optical properties of CdMgTe epitaxial layers: a variable-angle spectroscopic ellipsometry study,” J. Appl. Phys. 78, 3387–3391 (1995).
[CrossRef]

1992 (1)

D. W. Schubert, M. M. Kraus, R. Kenklies, C. R. Becker, and R. N. Bicknell-Tassius, “Composition and wavelength dependence of the refractive index in Cd1−xMnxTe epitaxial layers,” Appl. Phys. Lett. 60, 2192–2194 (1992).
[CrossRef]

1989 (1)

S. Adachi, “Optical dispersion relations for GaP, GaAs, GaSb, InP, InAs, InSb, AlxGa1−xAs, and In1−xGaxAsyP1−y,” J. Appl. Phys. 66, 6030–6040 (1989).
[CrossRef]

1987 (1)

J. C. Bhattacharya, “Refractive index measurement,” Opt. Laser Technol. 19, 29–32 (1987).
[CrossRef]

1985 (1)

L. Kowalczyk, “Second harmonic generation in Cd1−xMnxTe,” J. Cryst. Growth 72, 389–392 (1985).

1976 (1)

1964 (1)

D. T. F. Marple, “Refractive index of ZnSe, ZnTe, and CdTe,” J. Appl. Phys. 35, 539–542 (1964).
[CrossRef]

Adachi, S.

S. Adachi, “Optical dispersion relations for GaP, GaAs, GaSb, InP, InAs, InSb, AlxGa1−xAs, and In1−xGaxAsyP1−y,” J. Appl. Phys. 66, 6030–6040 (1989).
[CrossRef]

Becker, C. R.

D. W. Schubert, M. M. Kraus, R. Kenklies, C. R. Becker, and R. N. Bicknell-Tassius, “Composition and wavelength dependence of the refractive index in Cd1−xMnxTe epitaxial layers,” Appl. Phys. Lett. 60, 2192–2194 (1992).
[CrossRef]

Becouarn, L.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94, 6447–6455 (2003).
[CrossRef]

Bertin, F.

M. Luttmann, F. Bertin, and A. Chabli, “Optical properties of CdMgTe epitaxial layers: a variable-angle spectroscopic ellipsometry study,” J. Appl. Phys. 78, 3387–3391 (1995).
[CrossRef]

Bhattacharya, J. C.

J. C. Bhattacharya, “Refractive index measurement,” Opt. Laser Technol. 19, 29–32 (1987).
[CrossRef]

Bicknell-Tassius, R. N.

D. W. Schubert, M. M. Kraus, R. Kenklies, C. R. Becker, and R. N. Bicknell-Tassius, “Composition and wavelength dependence of the refractive index in Cd1−xMnxTe epitaxial layers,” Appl. Phys. Lett. 60, 2192–2194 (1992).
[CrossRef]

Bok, J.

P. Hlidek, J. Bok, J. Franc, and R. Grill, “Refractive index of CdTe: spectral and temperature dependence,” J. Appl. Phys. 90, 1672–1674 (2001).
[CrossRef]

Bolotnikov, A. E.

A. Hossain, V. Yakimovich, A. E. Bolotnikov, K. Bolton, G. S. Camarda, Y. Cui, J. Franc, R. Gul, K.-H. Kim, H. Pittman, G. Yang, R. Herpst, and R. B. James, “Development of cadmium magnesium telluride (Cd1−xMgxTe) for room temperature X- and gamma-ray detectors,” J. Cryst. Growth 379, 34–40 (2013).
[CrossRef]

Bolton, K.

A. Hossain, V. Yakimovich, A. E. Bolotnikov, K. Bolton, G. S. Camarda, Y. Cui, J. Franc, R. Gul, K.-H. Kim, H. Pittman, G. Yang, R. Herpst, and R. B. James, “Development of cadmium magnesium telluride (Cd1−xMgxTe) for room temperature X- and gamma-ray detectors,” J. Cryst. Growth 379, 34–40 (2013).
[CrossRef]

Burger, A.

A. Mycielski, A. Burger, M. Sowinska, M. Groza, A. Szadkowski, P. Wojnar, B. Witkowska, W. Kaliszek, and P. Siffert, “Crystal growth and characterization of Cd0.8Mn0.2Te using vertical Bridgman method,” Phys. Status Solidi C 5, 1578–1585 (2005).

Camarda, G. S.

A. Hossain, V. Yakimovich, A. E. Bolotnikov, K. Bolton, G. S. Camarda, Y. Cui, J. Franc, R. Gul, K.-H. Kim, H. Pittman, G. Yang, R. Herpst, and R. B. James, “Development of cadmium magnesium telluride (Cd1−xMgxTe) for room temperature X- and gamma-ray detectors,” J. Cryst. Growth 379, 34–40 (2013).
[CrossRef]

Cha, M.

Chabli, A.

M. Luttmann, F. Bertin, and A. Chabli, “Optical properties of CdMgTe epitaxial layers: a variable-angle spectroscopic ellipsometry study,” J. Appl. Phys. 78, 3387–3391 (1995).
[CrossRef]

Choi, H. J.

Cui, Y.

A. Hossain, V. Yakimovich, A. E. Bolotnikov, K. Bolton, G. S. Camarda, Y. Cui, J. Franc, R. Gul, K.-H. Kim, H. Pittman, G. Yang, R. Herpst, and R. B. James, “Development of cadmium magnesium telluride (Cd1−xMgxTe) for room temperature X- and gamma-ray detectors,” J. Cryst. Growth 379, 34–40 (2013).
[CrossRef]

DiRocco, C.

Eom, T. B.

Eyres, L. A.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94, 6447–6455 (2003).
[CrossRef]

Fejer, M. M.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94, 6447–6455 (2003).
[CrossRef]

Franc, J.

A. Hossain, V. Yakimovich, A. E. Bolotnikov, K. Bolton, G. S. Camarda, Y. Cui, J. Franc, R. Gul, K.-H. Kim, H. Pittman, G. Yang, R. Herpst, and R. B. James, “Development of cadmium magnesium telluride (Cd1−xMgxTe) for room temperature X- and gamma-ray detectors,” J. Cryst. Growth 379, 34–40 (2013).
[CrossRef]

P. Hlidek, J. Bok, J. Franc, and R. Grill, “Refractive index of CdTe: spectral and temperature dependence,” J. Appl. Phys. 90, 1672–1674 (2001).
[CrossRef]

Gerard, B.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94, 6447–6455 (2003).
[CrossRef]

Gillen, G. D.

Grill, R.

P. Hlidek, J. Bok, J. Franc, and R. Grill, “Refractive index of CdTe: spectral and temperature dependence,” J. Appl. Phys. 90, 1672–1674 (2001).
[CrossRef]

Groza, M.

A. Mycielski, A. Burger, M. Sowinska, M. Groza, A. Szadkowski, P. Wojnar, B. Witkowska, W. Kaliszek, and P. Siffert, “Crystal growth and characterization of Cd0.8Mn0.2Te using vertical Bridgman method,” Phys. Status Solidi C 5, 1578–1585 (2005).

Guha, S.

Gul, R.

A. Hossain, V. Yakimovich, A. E. Bolotnikov, K. Bolton, G. S. Camarda, Y. Cui, J. Franc, R. Gul, K.-H. Kim, H. Pittman, G. Yang, R. Herpst, and R. B. James, “Development of cadmium magnesium telluride (Cd1−xMgxTe) for room temperature X- and gamma-ray detectors,” J. Cryst. Growth 379, 34–40 (2013).
[CrossRef]

Hanning, E. A.

Harris, J. S.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94, 6447–6455 (2003).
[CrossRef]

Herpst, R.

A. Hossain, V. Yakimovich, A. E. Bolotnikov, K. Bolton, G. S. Camarda, Y. Cui, J. Franc, R. Gul, K.-H. Kim, H. Pittman, G. Yang, R. Herpst, and R. B. James, “Development of cadmium magnesium telluride (Cd1−xMgxTe) for room temperature X- and gamma-ray detectors,” J. Cryst. Growth 379, 34–40 (2013).
[CrossRef]

Hlidek, P.

P. Hlidek, J. Bok, J. Franc, and R. Grill, “Refractive index of CdTe: spectral and temperature dependence,” J. Appl. Phys. 90, 1672–1674 (2001).
[CrossRef]

Hossain, A.

A. Hossain, V. Yakimovich, A. E. Bolotnikov, K. Bolton, G. S. Camarda, Y. Cui, J. Franc, R. Gul, K.-H. Kim, H. Pittman, G. Yang, R. Herpst, and R. B. James, “Development of cadmium magnesium telluride (Cd1−xMgxTe) for room temperature X- and gamma-ray detectors,” J. Cryst. Growth 379, 34–40 (2013).
[CrossRef]

Icenogle, H. W.

James, R. B.

A. Hossain, V. Yakimovich, A. E. Bolotnikov, K. Bolton, G. S. Camarda, Y. Cui, J. Franc, R. Gul, K.-H. Kim, H. Pittman, G. Yang, R. Herpst, and R. B. James, “Development of cadmium magnesium telluride (Cd1−xMgxTe) for room temperature X- and gamma-ray detectors,” J. Cryst. Growth 379, 34–40 (2013).
[CrossRef]

Jenkins, F. A.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1957).

Ju, J. J.

Kaliszek, W.

A. Mycielski, A. Burger, M. Sowinska, M. Groza, A. Szadkowski, P. Wojnar, B. Witkowska, W. Kaliszek, and P. Siffert, “Crystal growth and characterization of Cd0.8Mn0.2Te using vertical Bridgman method,” Phys. Status Solidi C 5, 1578–1585 (2005).

Kenklies, R.

D. W. Schubert, M. M. Kraus, R. Kenklies, C. R. Becker, and R. N. Bicknell-Tassius, “Composition and wavelength dependence of the refractive index in Cd1−xMnxTe epitaxial layers,” Appl. Phys. Lett. 60, 2192–2194 (1992).
[CrossRef]

Kim, K.-H.

A. Hossain, V. Yakimovich, A. E. Bolotnikov, K. Bolton, G. S. Camarda, Y. Cui, J. Franc, R. Gul, K.-H. Kim, H. Pittman, G. Yang, R. Herpst, and R. B. James, “Development of cadmium magnesium telluride (Cd1−xMgxTe) for room temperature X- and gamma-ray detectors,” J. Cryst. Growth 379, 34–40 (2013).
[CrossRef]

Kogelnik, H.

H. Kogelnik and T. Li, “Beams, Modes and Resonators,” in Handbook of Lasers with Selected Data on Optical Technology, R. Pressley, ed. (CRC Press, 1971), pp. 421–441.

Kowalczyk, L.

L. Kowalczyk, “Second harmonic generation in Cd1−xMnxTe,” J. Cryst. Growth 72, 389–392 (1985).

Kraus, M. M.

D. W. Schubert, M. M. Kraus, R. Kenklies, C. R. Becker, and R. N. Bicknell-Tassius, “Composition and wavelength dependence of the refractive index in Cd1−xMnxTe epitaxial layers,” Appl. Phys. Lett. 60, 2192–2194 (1992).
[CrossRef]

Kuo, P. S.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94, 6447–6455 (2003).
[CrossRef]

Lallier, E.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94, 6447–6455 (2003).
[CrossRef]

Levi, O.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94, 6447–6455 (2003).
[CrossRef]

Li, T.

H. Kogelnik and T. Li, “Beams, Modes and Resonators,” in Handbook of Lasers with Selected Data on Optical Technology, R. Pressley, ed. (CRC Press, 1971), pp. 421–441.

Lim, H. H.

Luttmann, M.

M. Luttmann, F. Bertin, and A. Chabli, “Optical properties of CdMgTe epitaxial layers: a variable-angle spectroscopic ellipsometry study,” J. Appl. Phys. 78, 3387–3391 (1995).
[CrossRef]

Ma, H.

X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).

Marple, D. T. F.

D. T. F. Marple, “Refractive index of ZnSe, ZnTe, and CdTe,” J. Appl. Phys. 35, 539–542 (1964).
[CrossRef]

Ming, H.

X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).

Moon, H. S.

Mycielski, A.

A. Mycielski, A. Burger, M. Sowinska, M. Groza, A. Szadkowski, P. Wojnar, B. Witkowska, W. Kaliszek, and P. Siffert, “Crystal growth and characterization of Cd0.8Mn0.2Te using vertical Bridgman method,” Phys. Status Solidi C 5, 1578–1585 (2005).

Pinguet, T. J.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94, 6447–6455 (2003).
[CrossRef]

Pittman, H.

A. Hossain, V. Yakimovich, A. E. Bolotnikov, K. Bolton, G. S. Camarda, Y. Cui, J. Franc, R. Gul, K.-H. Kim, H. Pittman, G. Yang, R. Herpst, and R. B. James, “Development of cadmium magnesium telluride (Cd1−xMgxTe) for room temperature X- and gamma-ray detectors,” J. Cryst. Growth 379, 34–40 (2013).
[CrossRef]

Platt, B. C.

Powers, P.

Schubert, D. W.

D. W. Schubert, M. M. Kraus, R. Kenklies, C. R. Becker, and R. N. Bicknell-Tassius, “Composition and wavelength dependence of the refractive index in Cd1−xMnxTe epitaxial layers,” Appl. Phys. Lett. 60, 2192–2194 (1992).
[CrossRef]

Schunemann, P. G.

Siffert, P.

A. Mycielski, A. Burger, M. Sowinska, M. Groza, A. Szadkowski, P. Wojnar, B. Witkowska, W. Kaliszek, and P. Siffert, “Crystal growth and characterization of Cd0.8Mn0.2Te using vertical Bridgman method,” Phys. Status Solidi C 5, 1578–1585 (2005).

Skauli, T.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94, 6447–6455 (2003).
[CrossRef]

Sowinska, M.

A. Mycielski, A. Burger, M. Sowinska, M. Groza, A. Szadkowski, P. Wojnar, B. Witkowska, W. Kaliszek, and P. Siffert, “Crystal growth and characterization of Cd0.8Mn0.2Te using vertical Bridgman method,” Phys. Status Solidi C 5, 1578–1585 (2005).

Sun, X.

X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).

Szadkowski, A.

A. Mycielski, A. Burger, M. Sowinska, M. Groza, A. Szadkowski, P. Wojnar, B. Witkowska, W. Kaliszek, and P. Siffert, “Crystal growth and characterization of Cd0.8Mn0.2Te using vertical Bridgman method,” Phys. Status Solidi C 5, 1578–1585 (2005).

Vodopyanov, K. L.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94, 6447–6455 (2003).
[CrossRef]

White, H. E.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1957).

Witkowska, B.

A. Mycielski, A. Burger, M. Sowinska, M. Groza, A. Szadkowski, P. Wojnar, B. Witkowska, W. Kaliszek, and P. Siffert, “Crystal growth and characterization of Cd0.8Mn0.2Te using vertical Bridgman method,” Phys. Status Solidi C 5, 1578–1585 (2005).

Wojnar, P.

A. Mycielski, A. Burger, M. Sowinska, M. Groza, A. Szadkowski, P. Wojnar, B. Witkowska, W. Kaliszek, and P. Siffert, “Crystal growth and characterization of Cd0.8Mn0.2Te using vertical Bridgman method,” Phys. Status Solidi C 5, 1578–1585 (2005).

Wolfe, W. L.

Xie, J.

X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).

Yakimovich, V.

A. Hossain, V. Yakimovich, A. E. Bolotnikov, K. Bolton, G. S. Camarda, Y. Cui, J. Franc, R. Gul, K.-H. Kim, H. Pittman, G. Yang, R. Herpst, and R. B. James, “Development of cadmium magnesium telluride (Cd1−xMgxTe) for room temperature X- and gamma-ray detectors,” J. Cryst. Growth 379, 34–40 (2013).
[CrossRef]

Yang, G.

A. Hossain, V. Yakimovich, A. E. Bolotnikov, K. Bolton, G. S. Camarda, Y. Cui, J. Franc, R. Gul, K.-H. Kim, H. Pittman, G. Yang, R. Herpst, and R. B. James, “Development of cadmium magnesium telluride (Cd1−xMgxTe) for room temperature X- and gamma-ray detectors,” J. Cryst. Growth 379, 34–40 (2013).
[CrossRef]

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X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).

Zelmon, D. E.

Zheng, Z.

X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).

Appl. Opt. (3)

Appl. Phys. Lett. (1)

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J. Cryst. Growth (2)

A. Hossain, V. Yakimovich, A. E. Bolotnikov, K. Bolton, G. S. Camarda, Y. Cui, J. Franc, R. Gul, K.-H. Kim, H. Pittman, G. Yang, R. Herpst, and R. B. James, “Development of cadmium magnesium telluride (Cd1−xMgxTe) for room temperature X- and gamma-ray detectors,” J. Cryst. Growth 379, 34–40 (2013).
[CrossRef]

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J. Opt. Soc. Am. B (1)

Opt. Express (1)

Opt. Laser Technol. (2)

X. Sun, H. Ma, H. Ming, Z. Zheng, J. Yang, and J. Xie, “The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method,” Opt. Laser Technol. 36, 163–166 (2004).

J. C. Bhattacharya, “Refractive index measurement,” Opt. Laser Technol. 19, 29–32 (1987).
[CrossRef]

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A. Mycielski, A. Burger, M. Sowinska, M. Groza, A. Szadkowski, P. Wojnar, B. Witkowska, W. Kaliszek, and P. Siffert, “Crystal growth and characterization of Cd0.8Mn0.2Te using vertical Bridgman method,” Phys. Status Solidi C 5, 1578–1585 (2005).

Other (4)

From Eq. (1), the refractive index is given by n=(1−Δz/d)−1. With the reasonable assumption that the thickness measurement errors are normally distributed and uncorrelated with Δz, the relative uncertainty δn/n in the refractive index is δnn=n−1(∂n∂dδd)2+(∂n∂ΔzδΔz)2=nd(Δzdδd)2+(δΔz)2.The uncertainty δΔz in the focal shift is given by δΔz=δzsample2+δznosample2≈δz2,where we have explicitly assumed that the focal position measurement error δz is unchanged by the presence of the sample.

H. Kogelnik and T. Li, “Beams, Modes and Resonators,” in Handbook of Lasers with Selected Data on Optical Technology, R. Pressley, ed. (CRC Press, 1971), pp. 421–441.

F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, 1957).

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